On each homework assignment, please write (i) your name, (ii) name of course, and (iii) homework number. You are allowed and encouraged to work together on homework. Yet, each student is expected to turn in their own work. In general, late homework will not be accepted. However, you are allowed to turn in **up to three late homework assignments with no questions asked**. When doing your homework, I encourage you to consult the Elements of Style for Proofs.

The following framework assumes that we will be in a remote setting. If we happen to return to face-to-face classes, we will adjust in a natural way. With a few exceptions, homework assignment will consist of two parts.

**Part 1:** Prior to the start of class, you will need to capture your handwritten work digitally and then upload a PDF to BbLearn. There are many free smartphone apps for doing this. I use TurboScan on my iPhone. Submitting your work prior to class allows me to see what you accomplished outside of class.

**Part 2:** During class, we will discuss most of the problems that are due that day. While we are discussing them, you should either annotate your work and/or take notes on separate paper. It’s expected that most of the work you did prior to class will need to be refined. It is your responsibility to process this in some way. Annotating your work or taking notes will increase the chances that you are processing the work in a meaningful way. If you choose to annotate your work, **please use a different color** than what you originally used to complete your assignment. After class, you will need to capture your annotations/notes digitally and then upload a PDF to BbLearn.

Unless otherwise indicated, submit each of the following assignments via BbLearn. I reserve the right to modify the assignment if the need arises. These exercises will form the basis of the student-led presentations.

**Homework 1:**Read the syllabus and write down 5 important items. Submit a PDF of your written work to the corresponding assignment on BbLearn.*Note:*All of the exam dates only count as a single item. (Due Friday, August 14)**Homework 2:**Create a free Discord account, accept the invite to our Discord server, and post something about yourself in the #introductions channel. (Due Friday, August 14)**Homework 3:**Read all of the Preface and Chapter 1: Introduction of the course notes. In addition, complete 2.1-2.11 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Friday, August 14)**Homework 4:**Complete 2.12-2.14 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Monday, August 17)**Homework 5:**Complete 2.17 and 2.18 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. In addition, brainstorm and write down a game plan for how you can display your work to the class (i.e., phone as a doc camera, write on iPad and share screen, share PDF of written work, Google Doc, other). (Due Wednesday, August 19)**Homework 6:**Complete 2.19-2.24, 2.26-2.28 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Friday, August 21)**Homework 7:**Complete 2.29, 2.31, 2.32, 2.34, 2.35 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Monday, August 24)**Homework 8:**Complete 2.36-2.41 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. In addition, watch the following three Socratica videos: (Due Wednesday, August 26)**Homework 9:**Complete 2.42-2.44, 2.47, 2.48 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Friday, August 28)**Homework 10:**Complete 2.49, 2.52, 2.55, 2.56 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. In addition, watch the following Socratica video: (Due Monday, August 31)**Homework 11:**Complete 2.57-2.60 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Wednesday, September 2)**Homework 12:**Complete 2.61-2.66 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Friday, September 4)**Homework 13:**Complete 2.67-2.69, 2.71, 2.72 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Wednesday, September 9)**Homework 14:**Complete 2.73. 2.74, 2.78-2.82 (optional: 2.75, 2.76, 2.77) in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Friday, September 11)**Homework 15:**Complete 3.1-3.3, 3.5 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Monday, September 14)**Homework 16:**Complete 3.6-3.13 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Wednesday, September 16)**Homework 17:**Review Theorem 3.24 and Problem 3.25 and then complete 3.26-3.30, 3.32. in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Monday, September 28)**Homework 18:**Complete 3.33-3.40 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Wednesday, September 30)**Homework 19:**Complete 3.41-3.45, 3.47-3.50 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Friday, October 2)**Homework 20:**Review Theorems 3.51 3.52 (these were on take-home exam under the guise of “wicked awesome”) and complete 3.53-3.57 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Monday, October 5)**Homework 21:**Complete 3.58 and 3.59 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Wednesday, October 7)**Homework 22:**Complete 3.60-3.62 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Friday, October 9)**Homework 23:**Complete 3.63-3.66 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Monday, October 12)**Homework 24:**Complete 4.1-4.12 in Chapter 4: Families of Groups and digest the surrounding text along the way. (Due Wednesday, October 14)**Homework 25:**Complete 4.13, 4.15, 4.17, 4.18, 4.20-4.23 in Chapter 4: Families of Groups and digest the surrounding text along the way. Be sure you review Theorems 4.16 and 4.19. (Due Friday, October 16)**Homework 26:**Complete 4.25-4.29 4.32, 4.33 in Chapter 4: Families of Groups and digest the surrounding text along the way. Be sure you review Theorem 4.24 along the way. (Due Monday, October 19)**Homework 27:**Complete 4.36-4.41 in Chapter 4: Families of Groups and digest the surrounding text along the way. (Due Wednesday, October 21)**Homework 28:**Complete 4.42, 4.43, 4.46, 4.47 in Chapter 4: Families of Groups and digest the surrounding text along the way. Be sure to read Theorems 4.44 and 4.45. I’ll likely put these on Part 2 of Exam 2. You can use these results in the problems that follow. (Due Friday, October 23)**Homework 29:**Complete 4.86, 4.87, 4.90-4.94 in Chapter 4: Families of Groups and digest the surrounding text along the way. (Due Wednesday, November 4)**Homework 30:**Complete 4.100, 4.102, 4.104, 4.106-4.110, 4.112 in Chapter 4: Families of Groups and digest the surrounding text along the way. (Due Friday, November 6)**Homework 31:**Complete 4.113-4.117 in Chapter 4: Families of Groups and digest the surrounding text along the way. (Due Monday, November 9)**Homework 32:**Read all of Chapter 5 and then complete 5.5-5.8, 5.17, 5.18, 5.27, 5.28, 5.31 in Chapter 5: Cosets, Lagrange’s Theorem, and Normal Subgroups. (Due Friday, November 13)**Homework 33:**Read all of Section 6.1 and then complete 6.13, 6.18, 6.20, 6.26, 6.27, 6.28 in Chapter 6: Products and Quotients of Groups. (Due Monday, November 16)**Homework 34:**Complete 6.33, 6.34 and do your best to complete 7.16 in Chapter 6: Products and Quotients of Groups and Chapter 7: Homomorphisms and the Isomorphism Theorems, respectively. (Due Wednesday, November 18)

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Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.